Logitech recently introduced PowerPlay, a new wireless charging technology. It's compatible with the G903 and G703 Lightspeed mice and works via a mousepad that plugs into a USB port.
Interestingly, it appears that PowerPlay may (unofficially) be compatible with other mice too. Legit Reviews discovered that the Logitech G403 seems to pair just fine with the PowerPlay charging system. The reviewer notes the mouse wirelessly recharged via PowerPlay and he contacted Logitech for a bit more information.
Logitech's response was that this is a feature that is not officially supported. It's a use-at-your-own risk situation, Logitech wouldn't really confirm whether it's safe to use.
This is a use at your own risk scenario and I have only had this test setup for less than a week, total, so I can’t comment on long-term results, yet. After speaking with my contact at Logitech, he explained that while PowerPlay wireless charging may work with the G403 Wireless, Logitech doesn’t officially support it and any damage or issues that may arise from using PowerPlay with the G403 Wireless.